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An Efficient Iterative Scheme Using Family of Chebyshev's Operations
Mathematical Problems in Engineering (2015)
Abstract

This paper presents an efficient iterative method originated from the family of Chebyshev's operations for the solution of nonlinear problems. For this aim, the product operation matrix of integration is presented, and therefore the operation of derivative is developed by using Chebyshev wavelet functions of the first and second kind, initially. Later, Chebyshev's iterative method is improved by approximation of the first and second derivatives. The analysis of convergence demonstrates that the method is at least fourth-order convergent. The effectiveness of the proposed scheme is numerically and practically evaluated. It is concluded that it requires the less number of iterations and lies on the best performance of the proposed method, especially for highly varying nonlinear problems.

Keywords
  • newtons method,
  • wavelet,
  • equations
Publication Date
2015
Publisher Statement
Cf3da Times Cited:0 Cited References Count:18
Citation Information
"An Efficient Iterative Scheme Using Family of Chebyshev's Operations" Mathematical Problems in Engineering (2015)
Available at: http://works.bepress.com/facultyofengineering_universityofmalaya/4/